Topological Queries Research Articles

Compact representations of spatial hierarchical structures with support for topological queries

Among different spatial data models, the topological model for spatial regions explicitly represents common boundaries. This model pursues the efficiency of topology-related queries and the elimination of data redundancy. This paper proposes several space-efficient data structures to support access to the topological representation of two-dimensional regions that are organized in a multi-granular or hierarchical structure, such as the political and administrative partition of a country. In the context of these hierarchies, we focus on queries that search for inclusion, disjointness, and adjacency between regions. The proposed structures build upon compact planar graph embeddings, which show to have a good trade-off between space and time.

Topological Access Methods for Spatial and Spatiotemporal Data

In order to perform topological queries on geographic data, it is necessary to first develop a topological access method (TOAM). Using the fact that any (incidence or other binary) relation produces a topology which includes the common usage of topology for spatial or spatiotemporal data, here, such a TOAM is developed on the basis of the previously applied concept of Property Graph used in order to manage topological information in data of any dimension, whether time dependent or not. As a matter of fact, it is necessary to have a TOAM in order to query such a graph, and also to have data which are topologically consistent in a certain sense. While the rendering of topological consistency was the concern of previous work, here, the aim is to develop a methodology which builds on this concept. In the end, an experimental test of this approach on a small city model is performed. It turned out that the Euler characteristic, a well-known topological invariant, can be helpful for the initial data validation. Practically, this present theoretical work is seen to be necessary in view of future innovative applications, e.g., in the context of city model simulations, including distributed geo-processing.

EFFICIENT SPATIO-TEMPORAL MODELLING TO ENABLE TOPOLOGICAL ANALYSIS

Abstract. Time-dependent analysis scenarios such as heat, wind or flood analysis in cities and in landscapes need a correct and consistent modelling of geometry and topology over time. However, hitherto efficient time-dependent geometry models and topological analysis based on a mathematically sound theory were neglected when modelling objects in the built and natural environment. This is surprising as incorrect topological relationships over time such as not fitting neighbourhoods of surfaces or solids inevitably lead to wrong analysis results. In this paper we propose the combination of a spatio-temporal geometry model together with a topological schema to provide accessible and consistent objects over time. Where an efficient spatio-temporal geometry model reduces redundant geometric data and enables spatio-temporal queries, an efficient topological model minimizes the number of relations as far as possible and enables robust topological queries. The geometry model uses the concepts of point tubes, delta storage as well as net components and pre- and post-objects to enable the change of geometry and topology over time for natural structures, e.g., digital terrain models (DTM). Geometry here are the boundary and interior coordinates of the objects whereas topology here is interpreted in a wider sense than only focusing on geometrically induced topology to maintain topological consistency by the management of incidence relations. In addition, the topological schema introduces three basic bidirectional relation types to manage aggregations, abstractions and incidences in order to provide a general abstract topological schema for the management of complex intra- and inter-related spatio-temporal objects to enable the modelling of consistent complex topology over time. Finally, a conclusion is given highlighting the applicability of the approach and future research.

Navigating planar topologies in near-optimal space and time

We show that any embedding of a planar graph can be encoded succinctly while efficiently answering a number of topological queries near-optimally. More precisely, we build on a succinct representation that encodes an embedding of m edges within 4m bits, which is close to the information-theoretic lower bound of about 3.58m. With 4m+o(m) bits of space, we show how to answer a number of topological queries relating nodes, edges, and faces, most of them in any time in ω(1). Indeed, 3.58m+o(m) bits suffice if the graph has no self-loops and no nodes of degree one. Further, we show that with O(m) bits of space we can solve all those operations in O(1) time.

A semantic graph database for the interoperability of 3D GIS data

In the last decades, the use of information management systems in the building data processing led to radical changes to the methods of data production, documentation and archiving. In particular, the possibilities, given by these information systems, to visualize the 3D model and to formulate queries have placed the question of the information sharing in digital format. The integration of information systems represents an efficient solution for defining smart, sustainable and resilient projects, such as conservation and restoration processes, giving the possibilities to combine heterogeneous data. GIS provides a robust data storage system, a definition of topological and semantic relationships and spatial queries. 3D GIS makes possible the creation of three-dimensional model in a geospatial context. To promote the interoperability of GIS data, the present research aims first to analyse methods of conversion in CityGML and IndoorGML model, defining an ontological domain. This has led to the creation of a new enriched model, based on connections among the different elements of the urban model in GIS environment, and to the possibility to formulate queries based on these relations. The second step consists in collecting all data translated into a specific format that fill a graph database in a semantic web environment, while maintaining those relationships. The semantic web technology represents an efficient tool of interoperability that leaves open the possibility to import BIM data in the same graph database and to join both GIS and BIM models. The outcome will offer substantial benefits during the entire project life cycle. This methodology can also be applied to cultural heritage where the information management plays a key role.

Tetrahedral Trees

We address the problem of performing efficient spatial and topological queries on large tetrahedral meshes with arbitrary topology and complex boundaries. Such meshes arise in several application domains, such as 3D Geographic Information Systems (GISs), scientific visualization, and finite element analysis. To this aim, we propose Tetrahedral trees , a family of spatial indexes based on a nested space subdivision (an octree or a kD-tree) and defined by several different subdivision criteria. We provide efficient algorithms for spatial and topological queries on Tetrahedral trees and compare to state-of-the-art approaches. Our results indicate that Tetrahedral trees are an improvement over R * -trees for querying tetrahedral meshes; they are more compact, faster in many queries, and stable at variations of construction thresholds. They also support spatial queries on more general domains than topological data structures, which explicitly encode adjacency information for efficient navigation but have difficulties with domains with a non-trivial geometric or topological shape.

DBTree: Very large phylogenies in portable databases

Abstract Growing numbers of large phylogenetic syntheses are being published. Sometimes as part of a hypothesis testing framework, sometimes to present novel methods of phylogenetic inference, and sometimes as a snapshot of the diversity within a database. Commonly used methods to reuse these trees in scripting environments have their limitations. I present a toolkit that transforms data presented in the most commonly used format for such trees into a database schema that facilitates quick topological queries. Specifically, the need for recursive traversal commonly presented by schemata based on adjacency lists is largely obviated. This is accomplished by computing pre‐ and post‐order indexes and node heights on the topology as it is being ingested. The resulting toolkit provides several command line tools to do the transformation and to extract subtrees from the resulting database files. In addition, reusable library code with object–relational mappings for programmatic access is provided. To demonstrate the utility of the general approach I also provide database files for trees published by Open Tree of Life, Greengenes, D‐PLACE, PhyloTree, the NCBI taxonomy and a recent estimate of plant phylogeny. The database files that the toolkit produces are highly portable (either as SQLite or tabular text) and can readily be queried, for example, in the R environment. Programming languages with mature frameworks for object‐relational mapping and phylogenetic tree analysis, such as Python, can use these facilities to make much larger phylogenies conveniently accessible to researcher programmers.

DORMAN: Database of Reconstructed MetAbolic Networks.

Genome-scale reconstructed metabolic networks have provided an organism specific understanding of cellular processes and their relations to phenotype. As they are deemed essential to study metabolism, the number of organisms with reconstructed metabolic networks continues to increase. This everlasting research interest lead to the development of online systems/repositories that store existing reconstructions and enable new model generation, integration, and constraint-based analyses. While features that support model reconstruction are widely available, current systems lack the means to help users who are interested in analyzing the topology of the reconstructed networks. Here, we present the Database of Reconstructed Metabolic Networks - DORMAN. DORMAN is a centralized online database that stores SBML-based reconstructed metabolic networks published in the literature, and provides web-based computational tools for visualizing and analyzing the model topology. Novel features of DORMAN are (i) interactive visualization interface that allows rendering of the complete network as well as editing and exporting the model, (ii) hierarchical navigation that provides efficient access to connected entities in the model, (iii) built-in query interface that allow posing topological queries, and finally, and (iv) model comparison tool that enables comparing models with different nomenclatures, using approximate string matching. DORMAN is online and freely accessible at http://ciceklab.cs.bilkent.edu.tr/dorman.

C-tree: efficient cell-based indexing of indoor mobile objects

With the increasing popularity of indoor positioning system technologies, many applications have become available that allow moving objects to be monitored and queried on the basis of their indoor locations. At the center of these applications is a data structure that is used for indexing the moving objects. For most of the current applications, the indexing is based on certain modifications of methods from the established research area of indexing objects moving in outdoor spaces. But the approach to indexing objects moving in indoor spaces should be more radically different. The nature of indoor spaces, which essentially consist of cells and connections between cells, and the concept of cell-based adjacency, as opposed to metric-based adjacency, require a significantly different focus and approach. In this paper, we present a cell-based index structure, which is called the C-tree (‘C’ for ‘cell’), for efficiently grouping and managing updates of moving objects in indoor spaces. The C-tree can efficiently serve indoor spatial queries, topological queries, adjacency queries and density-based queries. In addition, as shown in the paper, the density of indoor cells can play an important role in the performance of the index data structure. Taking cell density into account, we extend the application of the C-tree to construct what is called a density-based index tree, which substantially improves the performance of the index structure when the indoor space contains high density cells.

Navigating intrinsic triangulations

We present a data structure that makes it easy to run a large class of algorithms from computational geometry and scientific computing on extremely poor-quality surface meshes. Rather than changing the geometry, as in traditional remeshing, we consider intrinsic triangulations which connect vertices by straight paths along the exact geometry of the input mesh. Our key insight is that such a triangulation can be encoded implicitly by storing the direction and distance to neighboring vertices. The resulting signpost data structure then allows geometric and topological queries to be made on-demand by tracing paths across the surface. Existing algorithms can be easily translated into the intrinsic setting, since this data structure supports the same basic operations as an ordinary triangle mesh (vertex insertions, edge splits, etc. ). The output of intrinsic algorithms can then be stored on an ordinary mesh for subsequent use; unlike previous data structures, we use a constant amount of memory and do not need to explicitly construct an overlay mesh unless it is specifically requested. Working in the intrinsic setting incurs little computational overhead, yet we can run algorithms on extremely degenerate inputs, including all manifold meshes from the Thingi10k data set. To evaluate our data structure we implement several fundamental geometric algorithms including intrinsic versions of Delaunay refinement and optimal Delaunay triangulation, approximation of Steiner trees, adaptive mesh refinement for PDEs, and computation of Poisson equations, geodesic distance, and flip-free tangent vector fields.

Evaluation of Topological Consistency in CityGML

Boundary representation models are data models that represent the topology of a building or city model. This leads to an issue in combination with geometry, as the geometric model necessarily has an underlying topology. In order to allow topological queries to rely on the incidence graph only, a new notion of topological consistency is introduced that captures possible topological differences between the incidence graph and the topology coming from geometry. Intersection matrices then describe possible types of topological consistency and inconsistency. As an application, it is examined which matrices can occur as intersection matrices, and how matrices from topologically consistent data look. The analysis of CityGML data sets stored in a spatial database system then shows that many real-world data sets contain many topologically inconsistent pairs of polygons. It was observed that even if data satisfy the val3dity test, they can still be topologically inconsistent. On the other hand, it is shown that the ISO 19107 standard is equivalent to our notion of topological consistency. In the case when the intersection is a point, topological inconsistency occurs because a vertex lies on a line segment. However, the most frequent topological inconsistencies seem to arise when the intersection of two polygons is a line segment. Consequently, topological queries in present CityGML data cannot rely on the incidence graph only, but must always make costly geometric computations if correct results are to be expected.

Computing and querying strict, approximate, and metrically refined topological relations in linked geographic data

AbstractGeographic entities and the information associated with them play a major role in Web‐scale knowledge graphs such as Linked Data. Interestingly, almost all major datasets represent places and even entire regions as point coordinates. There are two key reasons for this. First, complex geometries are difficult to store and query using the current Linked Data technology stack to a degree where many queries take minutes to return or will simply time out. Second, the absence of complex geometries confirms a common suspicion among GIScientists, namely that for many everyday queries place‐based relational knowledge is more relevant than raw geometries alone. To give an illustrative example, the statement that the White House is in Washington, DC is more important for gaining an understating of the city than the exact geometries of both entities. This does not imply that complex geometries are unimportant but that (topological) relations should also be extracted from them. As Egenhofer and Mark (1995b) put it in their landmark paper on naive geography, topology matters, metric refines. In this work we demonstrate how to compute and utilize strict, approximate, and metrically refined topological relations between several geographic feature types in DBpedia and compare our results to approaches that compute result sets for topological queries on the fly.

A 25-Intersection Model for Representing Topological Relations between Simple Spatial Objects in 3-D Space

With the rapid development of the economy, urgent needs for 3-D Geographical Information System (GIS) have sprung up in many application fields. The precise expression of three-dimensional topological relations is the foundation of spatial analysis, topological query, and spatial reasoning in three-dimensional space. In this paper, we subdivide the topological part “boundary” into face, edge, and vertex and propose a 25-intersection model (25IM) to represent topological relations between two simple spatial objects (point, line, region, and body) in 3-D space. An object in the 25IM has five topological parts: vertex, edge, face, interior, and exterior. The classification of topological relations is simplified by merging contain/inside and cover/coveredby. The 25IM describes ten groups of topological relations: body/body, body/region, body/line, body/point, region/region, region/line, region/point, line/line, line/point, and point/point. The 25IM is demonstrated to be more expressive than the 9IM and the DE-9IM, especially in distinguishing the detail situations when one object meets/covers another object (e.g., two bodies meet/cover at vertex, edge, or face).

DETECTION AND EVALUATION OF TOPOLOGICAL CONSISTENCY IN CITYGML DATASETS

Abstract. The topological consistency of Boundary-Representation models, meaning here that the incidence graph is homeomorphic with the underlying topology of geographical data, is checked for several CityGML datasets, and a first classification of topological inconsistencies is performed. The analysis is carried out on a spatial database system into which the datasets have been imported. It is found that real-world datasets contain many topologically inconsistent pairs of intersecting polygons. Also data satisfying the ISO/OGC standards can still be topologically inconsistent. In the case when the intersection is a point, topological inconsistency occurs because a vertex lies on a line segment. However, the most frequent topological inconsistencies seem to arise when the intersection of two polygons is a line segment. Consequently, topological queries in present CityGML data cannot rely on the incidence graph only, but must always make costly geometric computations if correct results are to be expected.

Summarizing database schema based on graph partition

As the underlying database schemas become larger and more complex, it is difficult for casual users to understand the schemas and contents of databases. Therefore, it has become an essential task to summarize the database schemas. However, most prior approaches pay little attention to the topological characteristics between tables, ignore the effect of the user feedback, and fail to accurately predict the number of clusters in the output. This seriously limits their accuracy of schema summarization. To deal with the problems, we propose a new schema summarization method based on a graph partition mechanism. First, we introduce a novel strategy to construct a similarity matrix between tables, which is based on the topology compactness, content similarity and query logs. Then we provide a calculation formula for table importance and a detection scheme of the most important nodes in local areas. Both are used for selecting the initial cluster centers and predicting the number of clusters in the graph partition mechanism. Finally, we evaluate the proposed method over the database TPC-E, and results demonstrate that it achieves high performance in summarizing accuracy.

PANDA

A large body of research on subgraph query processing on large networks assumes that a query is posed in the form of a connected graph. Unfortunately, end users in practice may not always have precise knowledge about the topological relationships between nodes in a query graph to formulate a connected query. In this demonstration, we present a novel graph querying paradigm called partial topology-based network search and a query processing system called panda to efficiently find top-k matches of a partial topology query ( ptq ) in a single machine. A ptq is a disconnected query graph containing multiple connected query components . ptq s allow an end user to formulate queries without demanding precise information about the complete topology of a query graph. We demonstrate various innovative features of panda and its promising performance.

Vector Spatial Big Data Storage and Optimized Query Based on the Multi-Level Hilbert Grid Index in HBase

Faced with the rapid growth of vector data and the urgent requirement of low-latency query, it has become an important and timely challenge to effectively achieve the scalable storage and efficient access of vector big data. However, a systematic method is rarely seen for vector polygon data storage and query taking spatial locality into account in the storage schema, index construction and query optimization. In the paper, we focus on the storage and topological query of vector polygon geometry data in HBase, and the rowkey in the HBase table is the concatenation of the Hilbert value of the grid cell to which the center of the object entity’s MBR belongs, the layer identifier and the order code. Then, a new multi-level grid index structure, termed Q-HBML, that incorporates the grid-object spatial relationship and a new Hilbert hierarchical code into the multi-level grid, is proposed for improving the spatial query efficiency. Finally, based on the Q-HBML index, two query optimization strategies and an optimized topological query algorithm, ML-OTQ, are presented to optimize the topological query process and enhance the topological query efficiency. Through four groups of comparative experiments, it has been proven that our approach supports better performance.

Accelerated robust Boolean operations based on hybrid representations

Constructive Solid Geometry (CSG) is one of the popular techniques that is widely applied in 3D modeling. It combines primitive solids using Boolean operations. However, the trade-off between efficiency and robustness of Boolean evaluation is difficult to balance. Previous methods sacrifice either efficiency or robustness to achieve advantages in one perspective. Recent works attempt to achieve excellent performance in both aspects through replacing the conventional vertex-based representations (V-reps) with plane-based representations (P-reps) of polyhedrons. Different from V-reps, the P-reps use plane coefficients as meta-data and can lead to benign robustness. However, methods using P-reps have disadvantages in efficiency compared to methods using V-reps. In this paper, we proposed a Boolean evaluation approach that absorbs both the efficiency of V-reps based methods and robustness of P-reps based methods. We design a Boolean evaluation method combining P-reps with V-reps. The P-reps information is utilized for exact predicate computation while information in V-reps is collected for fast topology query and coarse tests. Our proposed approach is variadic: it evaluates a Boolean expression regarding multi-input meshes as a whole rather than a tree of decomposed binary operations. We conduct massive experiments and compare our results with those generated by the state-of-the-art methods. Experimental results show that our approach is robust for solid inputs and has advantages in performance compared to some previous non-robust methods.

A discrete global grid system for earth system modeling

ABSTRACTTo support Earth system modeling, we propose a discrete global grid system that expresses multi-resolution spatial data. Specifically, a unified coding model that expresses a grid of nodes, edges, and cells is constructed for a triangular discrete global grid system. To fulfill the requirements of practical applications, we design a code-based topological query method for this grid system and an algorithm to transform between grid codes and geographic coordinates. We evaluate the Global Finite Volume Community Ocean Model (Global-FVCOM) on the triangular discrete global grid system in the proposed uniform coding model. The ocean tidal waves simulated by the Global-FVCOM running on the coded grid are then compared with results obtained using a traditional irregular spherical grid system, and the results display comparable accuracy. The uniform coding model proposed in this paper provides a triangular discrete global grid system that can represent multi-resolution spatial data and can be used in Earth system models. This unified coding model can also be applied to the geographic coordinate system made up of latitudes and longitudes, as well as diamond and hexagonal grids.

Containment of queries for graphs with data

We consider the containment problem for regular queries with memory and regular queries with data tests: two recently proposed query languages for graph databases that, in addition to allowing the user to ask topological queries, also track how the data changes along paths connecting various points in the database. Our results show that the problem is undecidable in general. However, by allowing only positive data comparisons we find natural fragments with better static analysis properties: the containment problem is PSpace -complete in the case of regular queries with data tests and ExpSpace -complete in the case of regular queries with memory.